Update (at the risk of everyone here thinking I'm a total nutcase):
After conversations with two Clarion dealers, they convinced me that my problem -- the iPod always returning to track #1 -- was because I did not buy the Clarion unit specific for the Suzuki. Like an idiot, I took the bait, and ordered another Clarion EA1251B from a Suzuki dealer in Texas. It looked the same as the "generic" EA1251 I bought off of eBay, but, I thought optimistically, maybe the electronics inside are different.
Wrong. It does exactly the same thing: No matter what playlist I'm on, no matter what song I'm on, if I leave the car off for more than a few hours (I don't know the exact number, but it's more than two and less than eight), the iPod always returns to track #1. The only way to get back to the song I was last listening to is to push the up button on the Suzuki head unit -- and with my little 8GB Nano, that could be 1,200 pushes.
SO, I ripped the Clarion out, and put Tim's cable back in.
I now own *two* Clarion EA1251 units that I'd be happy to sell, but I live in Panama, so shipping would be a problem. Personally, I think Clarion released a dog with the EA1251; what's the point of having an iPod if you can't use or replicate any of the iPod's controls?
As a side note, I see that Clarion has come out with a new, smaller interface, called the CCA iPod. I don't know for sure if it will work with Suzuki head units, but it appears so. Crutchfield has it for $49.99; *however*, when I called Crutchfield the tech rep/sales guy I spoke with confirmed that it would behave the same as the EA1251: Power down, return to track #1. (Nice of him to be so honest, since I was ready to buy a *third* Clarion unit. Yes, I already admitted I'm hopelessly stupid.)
As I said before, with Tim's cable setup, I do not get the automatic power-off that the Clarion provides, and I do not get artist/title display in the Suzuki head unit, but the iPod is still completely in charge: I can pause, shuffle, change playlists, play by album or artist, move quickly to any song, and always start exactly where I left off (as long as I remember to push Pause on the iPod when I turn the car off).
Now if Tim could just figure out how to give me an auto-pause-and-power-down feature on his cable, I'd be completely, idiotically happy.